Asymptotic behavior of constrained local minimizers in finite elasticity

TL;DR

This paper investigates the asymptotic behavior of local minimizers in finite elasticity under curl constraints, connecting them to linear elastic equilibria with rotated loads.

Contribution

It introduces an approximation framework for constrained local minimizers in finite elasticity and characterizes their limits as linear elastic equilibria with rotations.

Findings

Local minimizers approximate linear elastic solutions under curl constraints

Inclusion of rotations in constraints leads to rotated load equilibria

Provides a rigorous link between finite and linear elasticity in constrained settings

Abstract

We provide an approximation result for the pure traction problem of linearized elasticity in terms of local minimizers of finite elasticity, under the constraint of vanishing average curl for admissible deformation maps. When suitable rotations are included in the constraint, the limit is shown to be the linear elastic equilibrium associated to rotated loads.